With respect you make a very broad statement. Would it not be a good thought to establish a middle-ground to create a bipartisan base to proceed on? For example, given we're all Americans here, do the individuals who receive equal treatment become influential over how measurable the inequality outcomes are for different groups? I am confused if you would explain what you mean and examples of, "...even if it results in measurable unequal outcomes for different groups."
Let me address your middle ground proposal. I'm going to use a colorful example in the hopes that it starkly illustrates my point. We have two positions, one position in this example is that people control their own bodies and the other position is that social isolation and involuntary abstinence are very harmful to people and society needs to help people afflicted with this outcome.
There are a lot of sexless Star Trek nerds in society and women absolutely do not want to have sex with them. We need to find a middle ground here so that these guys can be helped. To reach that middle ground we need women to move away from their absolutist position that they alone control who they have sex with. So, every Saturday of every week women must submit to having sex with any man who asks them. You see, we can reach a middle ground, women give up a little and sexless Star Trek nerds finally get to experience being with a woman.
The point here is that when you ask people to give up the right to be treated equally under the law in order to buy a benefit for a group who, also treated equally under the law, don't reach the same heights as others, you're violating sacred principles of fair treatment for those who you target to be the recipients of discrimination.
In my example above, women get to choose who they have sex with. If this exercise of a personal right results in nerdy Star Trek fans never being touched by the hand of a woman, then that's just something that society needs to accept.
You can't trade away one person's human rights in order to deliver a benefit to another person.
An example of what I'm talking about is the elimination of racial and gender quotas at universities, business contracting and employment hiring in order to achieve diversity targets or a diverse student body or a diverse workplace.